Information Bounds and Nonparametric Maximum Likelihood Estimation

Groeneboom, Piet; Wellner, Jon A.

doi:10.1007/978-3-0348-8621-5

Cited by 580 publications

(639 citation statements)

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“…The survival function modelled using an inverse Gaussian distribution was a good fit to the observed persistence data (described using a non-parametric function to accommodate interval and right censoring; see Groeneboom & Wellner (1992)) in the interval 0-25 years ( figure 1). The associated hazard function shows that the instantaneous probability of extinction was greatest in the years immediately following introduction and declined rapidly (figure 1), with most populations that became extinct persisting for less than 25 years.…”

Section: Resultsmentioning

confidence: 99%

Modelling population persistence on islands: mammal introductions in the New Zealand archipelago

Duncan

Forsyth

2006

Proc. R. Soc. B.

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Islands are likely to differ in their susceptibility to colonization or invasion due to variation in factors that affect population persistence, including island area, climatic severity and habitat modification. We tested the importance of these factors in explaining the persistence of 164 introductions of six mammal species to 85 islands in the New Zealand archipelago using survival analysis and model selection techniques. As predicted by the theory of stochastic population growth, extinction risk was the greatest in the period immediately following introduction, declining rapidly to low probability by ca 25 years. This suggests that initially small populations were at greatest risk of extinction and that populations which survived for 25 years were likely to persist subsequently for much longer. Islands in the New Zealand archipelago become colder and windier with increasing latitude, and the probability of mammal populations persisting on islands declined steeply with increasing latitude. Hence, our results suggest that climatic suitability was an important determinant of the outcome of these invasions. The form of the relationship between latitude and persistence probability differed among species, emphasizing that the outcome of colonization attempts is species-environment specific.

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Section: Resultsmentioning

confidence: 99%

Modelling population persistence on islands: mammal introductions in the New Zealand archipelago

Duncan

Forsyth

2006

Proc. R. Soc. B.

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“…Gehan (1965) and Turnbull (1974) and others considered doubly-censored data (where both left and right censoring occur simultaneously) and estimators for the distribution function have been developed. Groeneboom and Wellner (1992) and Geskus and Groeneboom (1996) studied the case of ''interval-censored'' data where one can only observe a censoring event and whether the time of the event of interest, say death, occurred before or after the occurrence of the censoring event. Nonparametric Maximum Likelihood Estimators (NPMLE) for the distribution of interest have been studied by various authors for all these cases.…”

Section: Introductionmentioning

confidence: 99%

Nonparametric estimation for middle-censored data

Jammalamadaka

Mangalam

2003

Journal of Nonparametric Statistics

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This paper provides the self-consistent estimator (SCE) and the nonparametric maximum likelihood estimator (NPMLE) for ''middle-censored'' data, in which a data value becomes unobservable if it falls within a random interval. We provide an algorithm to find the SCE and show that the NPMLE satisfies the self-consistency equation. We find a sufficient condition for the SCE to be concentrated on the uncensored observations. In addition, we find sufficient conditions for the consistency of the SCE and prove that consistency holds for the special case when one of the ends is a constant. Some simulation results and an illustrative example, using Danish melanoma data set, are provided.

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“…Gentleman and Vandal [3] discussed several methods and summarized them in two categories: those based on convex optimization and those based on finite mixture estimation. Two algorithms are compared in [11]: the iterative convex minorant (ICM), initially presented by Groeneboom and Wellner [12], and the vertex exchange method [13].…”

Section: Optimizing the Likelihoodmentioning

confidence: 99%

Most Likely Maximum Entropy for Population Analysis with Region-Censored Data

Bennani

Pronzato

Rendas

2015

Entropy

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The paper proposes a new non-parametric density estimator from region-censored observations with application in the context of population studies, where standard maximum likelihood is affected by over-fitting and non-uniqueness problems. It is a maximum entropy estimator that satisfies a set of constraints imposing a close fit to the empirical distributions associated with the set of censoring regions. The degree of relaxation of the data-fit constraints is chosen, such that the likelihood of the inferred model is maximal. In this manner, the estimator is able to overcome the singularity of the non-parametric maximum likelihood estimator and, at the same time, maintains a good fit to the observations. The behavior of the estimator is studied in a simulation, demonstrating its superior performance with respect to the non-parametric maximum likelihood and the importance of carefully choosing the degree of relaxation of the data-fit constraints. In particular, the predictive performance of the resulting estimator is better, which is important when the population analysis is done in the context of risk assessment. We also apply the estimator to real data in the context of the prevention of hyperbaric decompression sickness, where the available observations are formally equivalent to region-censored versions of the variables of interest, confirming that it is a superior alternative to non-parametric maximum likelihood in realistic situations.

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Information Bounds and Nonparametric Maximum Likelihood Estimation

Cited by 580 publications

References 0 publications

Modelling population persistence on islands: mammal introductions in the New Zealand archipelago

Modelling population persistence on islands: mammal introductions in the New Zealand archipelago

Nonparametric estimation for middle-censored data

Most Likely Maximum Entropy for Population Analysis with Region-Censored Data

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